{smcl}
{* 26mar2008}{...}
{cmd:help mata mm_gini()}
{hline}

{title:Title}

{pstd}
{bf:mm_gini() -- Gini coefficient}


{title:Syntax}

{p 8 12 2}
{it:real rowvector} {cmd:mm_gini(}{it:X} [{cmd:,}
{it:w}]{cmd:)}

{p 4 4 2}
where

{p 12 16 2}
{it:X}:  {it:real matrix} containing data (rows are observations, columns variables)

{p 12 16 2}
{it:w}:  {it:real colvector} containing weights


{title:Description}

{pstd}
{cmd:mm_gini(}{it:X}{cmd:,} {it:w}{cmd:)}
returns the Gini coefficient of each column of {it:X}.

{pstd}
{it:w} specifies the weights. Omit {it:w}, or specify {it:w} as 1 to obtain unweighted
results. Missing values in {it:X} or {it:w} are omitted
from the calculation.


{title:Remarks}

{pstd}The formula used in {cmd:mm_gini()} is

        G(x) = 2 * Cov0(x, F) / mu

{pstd}where mu is the mean of x. Let N denote the
number of observations (or sum of weights). Then,

        Cov0(x, F) = DCP(x, F) / N

{pstd}where DCP(x, F)
denotes the deviation cross product between x and its (adjusted)
empirical cumulative, F. To be precise, F is defined as

               1                     w_i
        F_i =  - * (    SUM  w_j  -  --- ),  i = 1,...,n
               W     x_j<=x_i         2

{pstd}where w_i are weights and W is the total sum of weights.

{pstd} Example:

        {com}: x = exp(invnormal(uniform(100,1)))
        {res}
        {com}: mm_gini(x, 1)
        {res}  .5158638536{txt}


{title:Conformability}

{pstd}
{cmd:mm_gini(}{it:x}{cmd:,} {it:w}{cmd:)}:
{p_end}
           {it:X}:  {it:n x k}
           {it:w}:  {it:n x 1} or {it:1 x 1}
      {it:result}:  {it:1 x k}


{title:Diagnostics}

{pstd}None.


{title:Source code}

{pstd}
{help moremata_source##mm_gini:mm_gini.mata}

{title:Author}

{pstd} Ben Jann, University of Bern, jann@soz.unibe.ch


{title:Also see}

{psee}
Online:  help for
{bf:{help mf_mean:[M-5] mean()}},
{bf:{help moremata}}
{p_end}

{psee}
Links to user-written programs:
{net "describe anogi, from(http://fmwww.bc.edu/RePEc/bocode/a)":anogi},
{net "describe egen_inequal, from(http://fmwww.bc.edu/RePEc/bocode/e)":egen_inequal},
{net "describe inequal7, from(http://fmwww.bc.edu/RePEc/bocode/i)":inequal7},
{net "describe sg115, from(http://www.stata.com/stb/stb51)":ineqerr},
{net "describe ginidesc, from(http://fmwww.bc.edu/RePEc/bocode/g)":ginidesc},
{net "describe descogin, from(http://fmwww.bc.edu/RePEc/bocode/d)":descogin},
{net "describe ineqdeco, from(http://fmwww.bc.edu/RePEc/bocode/i)":ineqdeco},
{net "describe ineqdec0, from(http://fmwww.bc.edu/RePEc/bocode/i)":ineqdec0}
